Mean, Variance, and Standard Deviation

• A mean is a number that attempts to represent all data gathered about a variable by getting the sum of all outcomes and dividing it by the number of outcomes.
• Variance and standard deviation on the other hand, measure how spread out of distribution of data is.
• The mean of a discrete random variable, also called the expected value, denoted by E(X), is the mean of the random variable if the experiment is done repeatedly.
• Expected value (E(X)) is equal to the weighted average of the elements x where each element is weighted by its respective probability.
• The Fair Game occurs if the expected value of the gain (or loss) equals 0. This means that the expected value of the total winnings is equal to the bet.
• The variance and standard deviation both describe how spread out or dispersed the data are in a probability distribution about the expected value or mean. A high variance and standard deviation mean that the values of the random variables are too different from one another. A low variance value means that the values are not too different from one another.
• Variance is computed by getting the sum of the weighted squared differences of the values from the expected value or mean.
• Standard deviation is computed by solving for the positive square root of the variance.